**ISC Paper 2017 **

**Physics **

**Maximum Marks: 70**

**Time allowed: Three hours**

**Candidates are allowed additional 15 minutes for only reading the paper. They must NOT start writing during this time****Answer all questions in Part I and ten questions from Part 11, choosing four questions from****Section A, three questions from Section B and three questions from Section C.****All working, including rough work, should be done on the same sheet as, and adjacent to, the rest of the answer.****The intended marks for questions or parts of questions are given in brackets [ ].****Material to be supplied: Long tables including Trigonometric functions.****A list of useful physical constants is given at the end of this paper.**

**Part – I (20 Marks) **

**(Answer all questions) **

**Question 1. **

**(a) Choose the correct alternative (a), (b), (c) or (d) for each of the questions given below: [5]**

**(i) The electrostatic potential energy of two point charges, 1 μC each, placed 1 metre apart in air is :**

**(a) 9 x 10 ^{3} J**

**(b) P x 10 ^{9} J**

**(c) 9 x 10 ^{-3}J**

**(d) 9 x 10 ^{-3} eV**

**Solution**

**Explanation: **

**(ii) A wire of resistance R ’ is cut into ‘n ’ equal parts. These parts are then connected in parallel with each other. The equivalent resistance of the combination is :**

**(a) nR**

**(b) R/n**

**(c) n/R ^{2}**

**(d) R/n ^{2}**

**Solution**

**Explanation: **

**(iii) Magnetic susceptibility of platinum is 0.0001. Its relative permeability is :**

**(a) 1.0000**

**(b) 0.9999**

**(c) 1.0001**

**(d) 0**

**Solution**

**Explanation: **

**(iv) When a light wave travels from air to glass :**

**(a) its wavelength decreases**

**(b) its wavelength increases**

**(c) there is no change in wavelength**

**(d) its frequency decreases.**

**Solution**

**Explanation: **

**(v) A radioactive substance decays to 1/16th of its initial mass in 40 days. The half life of the substance, in days, is:**

**(a) 20**

**(b) 10**

**(c) 5**

**(d) 2.5**

**Solution**

**Explanation: **

**B. Answer all questions given below briefly and to the point: [15]**

**(i) Maximum torque acting on the electric dipole of moment 3 × 10 ^{-29} Cm in a uniform electric field E is 6 × 10^{-25} Nm. Find E.**

**Solution**

**Explanation: **

**(ii) What is meant by drift speed of free electrons ?**

**Solution**

**Explanation: **

**(iii) On which conservation principle is Kirchhoff’s Second Law of electrical networks based ?**

**Solution**

**Explanation: **

**(iv) Calculate magnetic flux density of the magnetic field at the center of a circular coil of 50 turns, having radius of 0.5 m and carrying a current of 5 A. .**

**Solution**

**Explanation: **

**(v) An a.c. generator generates an emf ‘s’ where e = 314 Sin (50 πt) volt. Calculate the frequency of the emf ∈.**

**Solution**

**Explanation: **

**(vi) With what type of source of light are cylindrical wave fronts associated ?**

**Solution**

**Explanation: **

**(vii) How is fringe width of an interference pattern in Young’s double slit experiment affected if the two slits are brought closer to each other ?**

**Solution**

**Explanation: **

**(viii) In a regular prism, what is the relation between angle of incidence and angle of emergence when it is in the minimum deviation position ?**

**Solution**

**Explanation: **

**(ix) A converging lens of focal length 40 cm is kept in contact with a diverging lens of focal length 30 cm. Find the focal length of the combination.**

**Solution**

**Explanation: **

**(x) How can the spherical aberration produced by a lens be minimised ?**

**Solution**

**Explanation: **

**(xi) Calculate the momentum of a photon of energy 6 x 10 ^{-19} J.**

**Solution**

**Explanation: **

**(xii) According to Bohr, Angular momentum of an orbiting electron is quantised. ’ What is meant by this statement ?**

**Solution**

**Explanation: **

**(xiii) Why nuclear fusion reaction is also called thermo-nuclear reaction ?**

**Solution**

**Explanation: **

**(xiv) What is the minimum energy which a gamma ray photon must possess in order to produce electron-positron pair ?**

**Solution**

**Explanation: **

**(xv) Show the variation of voltage with time, for a digital signal.**

**Solution**

**Explanation: **

**Part – II (20 Marks) **

**Answer ten questions in this part, choosing four questions from Section A, three questions from Section B and three questions from Section C **

**Section-A **

**(Answer any four questions) **

**Question 2. **

**(a) Show that electric potential at a point P, at a distance ‘r’ from a fixed point charge Q, is given by: [4]**

**Solution**

**Explanation: **

**(b) Intensity of electric field at a perpendicular distance of 0.5 m from an infinitely long line charge having linear charge density (X) is 3.6 x 10 ^{3} Vm^{-1} . Find the value of λ . [1]**

**Solution**

**Explanation: **

**Question 3. **

**(a) Three capacitors C _{1}= 3 μF, C_{2}= 6 μF and C_{3}= 10 μF are connected to a 50 V battery as shown in the Figure 1 below : [3]**

**Calculate :**

**(i) The equivalent capacitance of the circuit between points A and B.**

**(ii) The charge on C _{1}**

**Solution**

**Explanation: **

**(b) Two resistors R _{1}= 60 Ω and R_{2}=90 Ω are connected in parallel. If electric power consumed by the resistor R_{1} is 15 W, calculate the power consumed by the resistor R_{2}. [2]**

**Solution**

**Explanation: **

**Question 4.**

**(a) Figure 2 below shows two resistors R _{1 }and R_{2} connected to a battery having an emf of 40 V and negligible internal resistance. A voltmeter having a resistance of 300 Ω is used to measure potential difference across R_{1}. Find the reading of the voltmeter. [3]**

**Solution**

**Explanation: **

**(b) A moving coil galvanometer has a coil of resistance 59 Ω. It shows a full scale deflection for a current of 50 mA. How will you convert it to an ammeter having a range of 0 to 3A ? [2]**

**Solution**

**Explanation: **

**Question 5. **

**(a) In a meter bridge circuit, resistance in the left hand gap is 2 Ω and an unknown resistance X is in the right hand gap as shown in Figure 3 below. The null point is found to be 40 cm from the left end of the wire. What resistance should be connected to X so that the new null point is 50 cm from the left end of the wire?**

**Solution**

**Explanation: **

**b) The horizontal component of earth’s magnetic field at a place is 1/√3 times the vertical component. Determine the angle of dip at that place.**

**Solution**

**Explanation: **

**Question 6. **

**(a) Using Ampere’s circuital law, obtain an expression for the magnetic flux density ‘B’ at a point X’ at a perpendicular distance ‘r from a long current carrying conductor. (Statement of the law is not required). [3]**

**Solution**

**Explanation: **

**(b) PQ is a long straight conductor carrying a current of 3A as shown in Figure 4 below. An electron moves with a velocity of 2 × 10 ^{7} ms^{-1} parallel to it. Find the force acting on the electron.**

**Solution**

**Explanation: **

**Question 7. **

**(a) (i) AB and CD are two parallel conductors kept 1 m apart and connected by a resistance R of 6 Ω as shown in Figure 5 below. They are placed in a magnetic field B =3 × 10 ^{-2} T which is perpendicular to the plane of the conductors and directed into the paper. A wire MN is placed over AB and CD and then made to slide with a velocity 2 ms^{-1 }. (Neglect the resistance of AB, CD. and MN). [3]**

**Calculate the induced current flowing through the resistor R.**

**(ii) In an ideal transformer, an output of 66 kV is required when an input voltage of 220 V is available. If the primary has 300 turns, how many turns should the secondary have ?**

**Solution**

**Explanation: **

**(b) In a series LCR circuit, obtain an expression for the resonant frequency. [2]**

**Solution**

**Explanation: **

**Section – B **

**(Answer any three questions) **

**Question 8. **

**(a) (i) State any one property which is common to all electromagnetic waves. [3]**

**(ii) Arrange the following electromagnetic waves in increasing order of their frequencies (i.e., begin with the lowest frequency) :**

**Visible light, γ-rays, X-rays, microwaves, radio waves, infrared radiations and ultraviolet radiations.**

**Solution**

**Explanation: **

**(b) (i) What is meant by diffraction of light ? [2]**

**(ii) In Fraunhofer diffraction, what kind of source of light is used and where is it situated?**

**Solution**

**Explanation: **

**Question 9. **

**(a) In Young’s double slit experiment using monochromatic light of wavelength 600 nm, 5th bright fringe is at a distance of 0.48 mm from the center of the pattern. If the screen is at a distance of 80 cm from the plane of the two slits, calculate : [3]**

**(i) Distance between the two slits.**

**(ii) Fringe width i.e., fringe separation.**

**Solution**

**Explanation: **

**(b) (i) State Brewster’s law.**

**(ii) Find Brewster’s [2]**

**Solution**

**Explanation: **

**Question 10. **

**(a) Find critical angle for glass and water pair, given refractive index of glass is 1.62 and that of water is 1.33. [2]**

**Solution**

**Explanation: **

**(b) Starting with an expression for refraction at a single spherical surface, obtain Lens Maker’s Formula. [3]**

**Solution**

**Explanation: **

**Question 11. **

**(a) A compound microscope consists of two convex lenses of focal length 2 cm and 5cm. When an object is kept at a distance of 2.1 cm from the objective, a virtual and magnified image is formed 25 cm from the eye piece. Calculate the magnifying power of the microscope. [3]**

**Solution**

**Explanation: **

**(b) (i) What is meant by resolving power of a telescope ?**

**(ii) State any one method of increasing the resolving power of an astronomical telescope. [2]**

**Solution**

**Explanation: **

**Section – C **

**(Answer any three questions) **

**Question 12. **

**(a) (i) Plot a labelled graph of /V _{s}/ where V_{s} is stopping potential versus frequency f of the incident radiation.**

**(ii) State how will you use this graph to determine the value of Planck’s constant. [3]**

**Solution**

**Explanation: **

**(b) (i) Find the de Broglie wavelength of electrons moving with a speed of 7 x 10 ^{6} ms^{-1} . [2]**

**(ii) Describe in brief what is observed when moving electrons are allowed to fall on a thin graphite film and the emergent beam falls on a fluorescent screen.**

**Solution**

**Explanation: **

**Question 13. **

**(a) Draw energy level diagram for hydrogen atom, showing first four energy levels corresponding to n = 1, 2, 3 and 4. Show transitions responsible for : [3]**

**(i) Absorption spectrum of Lyman series.**

**(ii) Emission spectrum of Balmer series.**

**Solution**

**Explanation: **

**(b) (i) Find maximum frequency of X-rays produced by an X-ray tube operating at a tube potential of 66 kV. [2]**

**(ii) State any one difference between characteristic X-rays and continuous X-rays.**

**Solution**

**Explanation: **

**Question 14. **

**(a) Obtain a relation between half life of a radioactive substance and decay constant (λ). [2]**

**Solution**

**Explanation: **

**(b) Calculate mass defect and binding energy per nucleon of, {_{10}^{20}Ne} given [3]**

**Solution**

**Explanation: **

**Question 15. **

**(a) With reference to a semiconductor diode, what is meant by :**

**(i) Forward bias**

**(ii) Reverse bias**

**(iii) Depletion region**

**Solution**

**Explanation: **

**(b) Draw a diagram to show how NAND gates can be combined to obtain an OR gate (Truth table is not required). [2]**

**Solution**

**Explanation: **